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The problem asks you to add two rational expressions:

\[
\frac{x}{x-3} + \frac{3x + 4}{x-3}
\]

Since both fractions have the same denominator \( x - 3 \), you can simply add the numerators. The denominator remains the same.

Step 1: Add the numerators:

\[
\frac{x + (3x + 4)}{x - 3} = \frac{x + 3x + 4}{x - 3}
\]

Step 2: Simplify the numerator:

\[
\frac{4x + 4}{x - 3}
\]

Step 3: Factor the numerator (if possible):

\[
\frac{4(x + 1)}{x - 3}
\]

So, the simplified form of the expression is:

\[
\frac{4(x + 1)}{x - 3}
\]

Let me know if you'd like further explanation or have questions! Here are 5 related questions you might consider:

1. What happens if the denominators are not the same?
2. How do you add rational expressions with different denominators?
3. Can this fraction be simplified further?
4. How do you factor quadratic expressions in the numerator?
5. What is the domain of the final expression?

**Tip:** Always check if the numerators can be factored to simplify expressions more easily.

Learn how to add and simplify rational expressions with common denominators, such as x/(x-3) + (3x+4)/(x-3). This detailed solution includes steps on combining numerators and factoring. Ideal for high school algebra students in Grades 9-12.

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